V2EX four-potential

Four-Potential

释义 Definition(中文)

四维势(four-potential)是相对论电磁学中的一个四矢量,把电势(标量势)与磁矢势合并为一个统一对象,常写作
\(A^\mu=(\phi/c,\ \mathbf{A})\),用于更简洁地表达洛伦兹协变的电磁理论与规范变换。(在不同教材中符号与因子约定可能略有差异。)

发音 Pronunciation(IPA)

/fr ptnl/

例句 Examples

In electromagnetism, the four-potential combines the scalar potential and the vector potential.
在电磁学中,四维势把标量势和矢势结合为一个整体。

Using the four-potential \(A^\mu\), Maxwell’s equations can be written in a Lorentz-covariant form, and gauge choices like the Lorenz gauge simplify calculations.
使用四维势 \(A^\mu\),麦克斯韦方程组可以写成洛伦兹协变的形式,而诸如洛伦兹规范之类的规范选择能简化计算。

词源 Etymology(中文)

该词由 **four-**(“四个/四维的”,对应狭义相对论的时空四维)与 potential(“势”,表示产生场的势函数)构成。它反映了20世纪相对论与电磁学融合后的表述习惯:把原来分开的电势 \(\phi\) 与磁矢势 \(\mathb{A}\) 统一为一个四维对象,以便在洛伦兹变换下具有清晰的变换性质。

相关词 Related Words

文学与经典著作中的用例 Literary Works

  • Classical Electrodynamics J. D. Jackson(以四维协变形式系统使用四维势与规范条件)
  • Introduction to Electrodynamics David J. Griffiths(在相对论电磁学章节引入四维势与场张量)
  • The Classical Theory of Fields Landau & Lifshitz(以场论视角讨论四维势与洛伦兹协变表达)
  • Spacetime and Geometry: An Introduction to General Relativity Sean Carroll(在场论/相对论语境中涉及四势与协变表述)
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